Scalar & vector quantities

A student went on a cycling journey that lasted for three days.

The student recorded information about the journey using a cycling app on a mobile phone.

At the start of the journey, the student travelled along a straight road to a road junction.

A map on the cycling app showed the road.

Figure 5 shows the map.

The scale of the map is 1 cm: 20 m

Calculate the distance travelled by the student between the start and the

road junction.

Use Figure 5.

The bicycle had a mass of 15 kg.

gravitational field strength = 9.8 N/kg

Calculate the weight of the bicycle.

Use the equation:

weight = mass × gravitational field strength

Figure 6 shows a velocity–time graph for a downhill part of the journey.

The gradient of the graph represents acceleration.

How does Figure 6 show that the acceleration was constant?

As the student accelerated downhill, the forward force on the student was 250 N.

The work done by the forward force was 4500 J.

Calculate the distance travelled as the student accelerated downhill.

Use the equation:

Most of the roads on the journey were not straight.

Figure 7 shows a map of the route taken for the whole journey.

The line in Figure 7 represents the total distance travelled when the student reached the end of the journey.

How does the total distance travelled compare with the magnitude of the displacement of the student from the start?

Tick () one box.

Why is distance a scalar quantity?

Tick () one box.

Figure 8 shows the distance travelled by the student each day.

Calculate the total distance travelled by the student.

Use Figure 8.

Professional rugby players wear a tracking device that measures their velocity and acceleration.

Figure 9 shows a player wearing a tracking device.

The player is tackling another player who is running with the ball.

Velocity and acceleration are both vector quantities.

What is a vector quantity?

Tick (✓) one box.

Which of the following is a vector quantity?

Tick (✓) one box.

Figure 10 shows a velocity–time graph for the player running with the ball.

Determine the acceleration of the player between 0 and 1.6 s.

Describe the motion of the player between 3.4 s and 3.6 s.

The force exerted on the player when she is tackled causes her to accelerate.

Write down the equation which links acceleration (a), mass (m) and resultant force (F).

The player accelerates at 25 m/s² when a resultant force of 1800 N acts on her.

Calculate the mass of the player.

The tracking device sends data to a computer during the game.

Suggest one advantage of the data being sent during the game.

Professional rugby players wear a tracking device that measures their velocity and acceleration. Figure 2 shows a player wearing a tracking device. The player is tackling another player who is running with the ball.

Velocity and acceleration are both vector quantities. What is a vector quantity? Tick (✓) one box.

Which of the following is a vector quantity? Tick (✓) one box.

Figure 3 shows a velocity–time graph for the player running with the ball.

Determine the acceleration of the player between 0 and 1.6 s.

Describe the motion of the player between 3.4 s and 3.6 s.

The force exerted on the player when she is tackled causes her to accelerate.

Write down the equation which links acceleration (a), mass (m) and resultant force (F).

The player accelerates at 25 m/s² when a resultant force of 1800 N acts on her. Calculate the mass of the player.

The tracking device sends data to a computer during the game. Suggest one advantage of the data being sent during the game.

Figure 1 shows a girl bowling a ball along a ten-pin bowling lane.

The girl is trying to knock down the ten pins at the end of the bowling lane. As the ball travels along the lane the velocity of the ball decreases.

Velocity is a vector. Which statement describes a vector? Tick (✓) one box.

Why does the velocity of the ball decrease as the ball travels along the lane? Tick (✓) one box.

The ball travels along the lane at an average speed of 4.5 m/s It takes the ball 4.0 seconds to travel the length of the lane. Calculate the length of the lane. Use the equation: distance travelled = speed × time

Figure 2 shows the ball hitting one of the pins.

Draw an arrow on Figure 2 to show the force of the pin on the ball.

The velocity of the pin changes from 0 to 12 m/s It takes 0.15 seconds for the velocity to change. Calculate the acceleration of the pin. Use the equation:

When the pin is struck it accelerates. Complete the sentences. Choose answers from the box. Each answer can be used once, more than once, or not at all.

The displacement of the pin from the girl. The mass of the pin. The kinetic energy of the pin.

Figure 8 shows a girl bowling a ball along a ten-pin bowling lane.

The girl is trying to knock down the ten pins at the end of the bowling lane.

Velocity is a vector quantity, speed is a scalar quantity. Describe what is meant by a vector quantity and a scalar quantity.

The bowling lane is horizontal. Explain why the bowling ball decelerates as it travels along the lane.

Figure 9 shows the bowling ball hitting one of the pins.

Write down the equation that links mass (m), momentum (p) and velocity (v).

The bowling ball has a velocity of 5.0 m/s when it hits the pin. The momentum of the bowling ball is 26 kg m/s Calculate the mass of the bowling ball.

Explain why the bowling ball slows down when it hits the pin. You should use ideas about momentum in your answer.

Figure 3 shows a gymnast on a piece of gymnastic equipment.

The equipment consists of two bars at different heights.

The gymnast exerts a downward force on the bar.

What is the size of the upward force acting on the gymnast from the bar?

Tick (✓) one box.

Why is the weight of the gymnast represented by an arrow?

Tick (✓) one box.

Figure 3 shows the weight of the gymnast acting from a point.

What name is given to this point?

Tick (✓) one box.

The gymnast has a mass of 45 kg

gravitational field strength = 9.8 N/kg

Calculate the weight of the gymnast.

Use the equation:

weight = mass × gravitational field strength

The gymnast swings from one bar to the other bar several times.

Describe how the gravitational potential energy store and the kinetic energy store of the gymnast change as she moves between the bars.

Falling on the crash mat reduces the average deceleration of the gymnast compared with falling on a hard surface.

Explain why reducing the deceleration is important to the gymnast.

Some quantities are scalars and some are vectors.

Which of the following quantities are scalars?

Tick (✓) two boxes.

Give the difference between a vector quantity and a scalar quantity.

Bumper cars are a fairground ride and are designed to bump into each other.

Figure 5 shows two bumper cars moving towards each other.

The momentum of each bumper car is shown by an arrow.

Give two factors that affect the momentum of each bumper car.

The bumper cars crash into each other and stop.

Explain why both bumper cars stop after the crash.